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Condition for Two Lines to Be Parallel

The value of ...

Question

The value of k if the lines $2 x + 5 y - 3 = 0 k x + 7 y + 5 = 0$ are parallel.

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Solution

$2 x + 5 y - 3 = 0 m = \frac{- 2}{5} k x + 7 y + 5 = 0 m = \frac{- k}{7}$
Since the lines are parallel, the slopes aare equal
$\frac{- 2}{5} = \frac{k}{7} k = \frac{- 14}{5}$

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